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Warp Scales
= Warp Factors: Eras and Ranges = Epiphany Trek How fast is fast? A question that has caused endless debates in fan circles. At least for my stories, these are the scales. Warp power is made possible by the leverage of a series of "second state" elements first discovered by Dr. Long du Hoc in 2052. These elements are necessary to control the energy flow in warp drive engines. The sub-dimensional Group 1A (Group 1A^2) elements are the most efficient for use in warp drives. Properly hydrogen^2, lithium^2, sodium^2, potassium^2, rubidium^2, cesium^2, and francium^2. The terminology "Dihydrogen" was popularized in the press at the time of discovery and has unfortunately made it back into the technical journals. Dihydrogen can be produced in the laboratory, and is relatively stable in use. Dilithium, the current element of choice. Disodium is a fragile and difficult element to find. As of yet only enough for a few elementary tests has been located. Elements further up the chart have not been identified under scientific conditions. Each jump in the element used renders a more efficient use of the energy produced to greater powers of the warp factor. The formula s=wf^x*c is used to figure the resulting speed for the use of a given element in the system. Differences in technology can vary this exact formula. Starfeet vessels currently using di-lithium are achieving wf^(10/3)c due to improvements in warp coils and drive controls. Warp factors are produced in nine ideal energy levels. Speeds between the ideal levels can be achieved, but with a greater drain on the ships resources. Warp 10, represents total efficiency and is technically unachievable. It is mistakenly referred to as "infinite speed". It is actually an energy use plateau that cannot be reached. A ship with a powerful drive can attain and pass what on the warp factor scale would be "warp ten", but not find the energy plateau. The practice of indicating the ship's speed in warp factors above 9 has been discontinued. A further group of sub-dimensional elements has been discovered. The Group 1a^3 series element have not proved exact analogs of the Group 1A, and Group 1A^2 elements. Attempts to use Trihydrogen or the even rarer Trilithium in starship drives have proven failures. OK, enough of the technobabble. See, I can do it too. Dihydrogen Warp Scale (power of 2) The following warp scale is the diHydrogen scale. I had not figured it out before the Romulan War Series. I might go back and correct them. From Earth, 1 ly in 6 mon 1 year 2 years days to days to Speed Times c n days radius radius radius Centauri Vulcan Wf 1 1 365. days .5 1 2 1,497 5,840 Wf 2 4 91.25 days 1.97 3.94 7.89 374 1460 Wf 3 9 40.5 days 4.4 8.8 17.7 166 648 Wf 4 16 22.8 days 7.89 15.78 31.57 93.48 364.8 Wf 5 25 14.2 days 12.67 25.35 50.7 58.22 227.2 Wf 6 36 10. days 18 36 72 41 160 Wf 7 49 7.44 days 24.2 48.4 96.7 30.5 119 Wf 8 64 5. days 36.5 73 146 21 80 Wf 9 81 4.5 days 40 80 160 18.5 72 DiLithium (TOS) Warp Scale (power of 3) This is the old and accepted scale for warp factors given in days gone by. Star Trek TOS never took it seriously, and the stories had them gallivanting all over the place regardless of how long or where the star or place was located. The 10,000 odd light years to the "edge" of the Galaxy from Earth would have taken a whopping 16,000 days or almost 44 years to accomplish. In short, consistency never got in the way of a good tale. Contrary to some fan notions this scale is in the Star Trek Writer's Guide, and not Fanon cooked up after the fact. From Earth, 1 ly in 6 mon 1 year 2 years days to days to Speed Times c n days radius radius radius Centauri Vulcan Wf 1 1 365. days 0.5 1 2 1,497 5,840 Wf 2 8 45. days 4 8 16 185 720 Wf 3 27 13. days 14 28 56 54 208 Wf 4 64 5. days 36.5 73 146 21 80 Wf 5 125 3. days 60.8 122 243 12 48 Wf 6 216 1.6 days 114 228 458 6.5 25.6 Wf 7 343 1.06 days 172 344 688 4.3 17 Wf 8 512 0.7 days 260 520 1,040 2.87 11.2 Wf 9 729 0.5 days 365 730 1,460 2 8 Wf 10 1,000 0.365 days 500 1,000 2,000 1.5 5.8 DiLithium Modified (TNG) (V=Wf*(10/3) to warp 9) The TNG table is the only one I have included the "nines" on. It's the only one where it matters or anyone really uses them I rounded a few figures, and changed the under explained asymptotic curve. My chart does not stay with the "explained" speeds passed warp 9.99, and then it is rounded off a bit to the slower side. I found a simple and workable solution to the 9s to infinity problem. Every time you add a decimal place, double the speed from the last full decimal place. I.E. If Wf 9 is 600c, then Wf 9.9 is 1200c and Wf 9.99 is 2400c etc. For the decimal warp factors between them divide the "9" factor by 9 and add it to each consecutively. This is not strictly a curve, but a series of arithmetic additions between geometric increases. It's ugly, but it functions. These are not the figures used "officially", but it should be workable. I don't know if these figures are anywhere close to what the show's technical writers had in mind, but they do not require a math degree to figure out or understand. This formula also works for any of the other warp scales for Warp Factors above Warp Factor 9. Warp factor 10 is not infinitely fast. It is an energy plateau that is never reached. From Earth, 1 ly in 6 mon 1 year 2 years days to days to Speed Times c n days radius radius radius Centauri Vulcan Wf 1 1 365 0.5 1 2 1,497 5,840 Wf 2 10 36.21 5 0 20 148 579 Wf 3 39 9.3 20 39 78 38 149 Wf 4 102 3.58 51 102 204 15 57 Wf 5 214 1.7 107 215 429 7 27 Wf 6 393 0.93 196 392 785 4 15 Wf 7 656 0.55 331 664 1,327 2 9 Wf 8 1,024 0.35 513 1,025 2,051 1.5 5.6 Wf 9 1,516 0.24 760 1,520 3,041 1 4 Wf 9.1 1,684 0.22 830 1,659 3,318 0.9 3.52 Wf 9.2 1,853 0.196 931 1,862 3,724 0.8 3.1 Wf 9.3 2,021 0.18 1,013 2,027 4,055 0.7 4 3 Wf 9.4 2,190 0.16 1,140 2,281 4,562 0.65 2.5 Wf 9.5 2,358 0.154 1,185 2,370 4,740 0.63 2.46 Wf 9.6 2,527 0.144 1,267 2,535 5,069 0.59 2.3 Wf 9.7 2,695 0.135 1,352 2,704 5,407 0.55 2.16 Wf 9.8 2,864 0.127 1,437 2,874 5,748 0.52 2 Wf 9.9 3,032 0.12 1,520 3,041 6,083 0.49 1.92 Wf 9.91 3,369 0.108 1,690 3,379 6,759 0.44 1.72 Wf 9.92 3,706 0.0984 1,855 3,709 7,419 0.4 1.57 Wf 9.93 4,043 0.09 2,027 4,055 8,111 0.369 1.44 Wf 9.94 4,380 0.083 2,198 4,397 8,795 0.34 1.32 Wf 9.95 4,716 0.077 2,370 4,740 9,480 0.31 1.23 Wf 9.96 5,053 0.072 2,534 5,069 10,138 0.29 1.15 Wf 9.97 5,390 0.067 2,723 5,448 10,895 0.27 1.07 Wf 9.98 5,727 0.063 2,896 5,794 11,587 0.258 1 Wf 9.99 6,064 0.06 3,041 6,083 12,166 0.246 0.96 Wf 9.999 12,128 0.03 6,083 12,166 24,333 0.123 0.48 Wf 9.9999 24,256 0.015 12,166 24,333 48,666 0.06 0.24 Wf 9.99999 48,512 0.0075 24,333 48,666 97,333 0.03 0.12 Disodium Warp Table (Power of 4) The DiSodium table. The numbers quickly pile up, but at this stage of the game the Federation (and anyone else) could really use the boost in technology. This is the case in Epiphany Trek. A source of diSodium has been located and the current generation of Starfleet vessel are taking advantage of the technology. From Earth, 1 ly in 6 mon 1 year 2 years days to days to Speed Times c n days radius radius radius Centauri Vulcan Wf 1 1 365. days .5 1 2 1,497 5,840 Wf 2 16 22.8 days 7.89 15.78 31.57 93.5 364.8 Wf 3 81 4.5 days 40 80 160 18.5 72 Wf 4 256 1.42 days 126.7 253.5 507 5.8 22.7 Wf 5 625 0.58 days 310.3 620.6 1241.3 2.38 9.28 Wf 6 1296 0.28 days 642.8 1285.7 2571.4 1.15 4.5 Wf 7 2401 0.15 days 1200 2400 4800 0.615 2.4 Wf 8 4096 0.089 days 2022.4 4044.9 8089.8 0.353 1.424 Wf 9 6561 0.055 days 3272.7 6545.4 1309.9 0.2255 0.88 Dipotassium "New Scale" (power of 5) This scale I first saw in the "technical" write up for the Enterprise-D model. Who ever thought this up didn't have a clue as to how the math would work out and how big the Galaxy was. It is presented as an interesting proposition. It does fit with DiPotassium. Such cultures as the Builders have ships that move at this scale. From Earth, 1 ly in 6 mon 1 year 2 years days to days to Speed Times c n days radius radius radius Centauri Vulcan Wf 1 1 365 0.5 1 2 1,497 5,840 Wf 2 32 11.4 16 32 64 46.7 182.4 Wf 3 243 1.46 250 500 1,000 5.9 23.36 Wf 4 1,024 0.35 521 1,042 2,084 1.43 5.6 Wf 5 3,125 0.1168 1,562 3,125 6,250 0.47 1.86 Wf 6 7,776 0.046 3,967 7,935 15,859 0.18 0.736 Wf 7 16,807 0.0217 8,410 16,820 33,640 0.088 0.347 Wf 8 32,768 0.011 16,591 33,182 66,363 0.045 0.176 Wf 9 52,049 0.007 26,071 52,143 104,286 0.028 0.112 Wf 10 100,000 0.00365 50,000 100,000 200,000 0.014 0.056 Other A few more figures to place some relevance on the numbers above. 0.1 days = 2 hours 24 minutes 0.01 days = 14 minutes, 24 seconds 0.001 days = 1 minute, 2.42 seconds Distance to Centauri is assumed to be 4.1 ly Distance to Vulcan is assumed to be 16 ly The Speed of Light in a vacuum is 186,262 miles per second (299,792km/sec). There are 31,536,000 seconds in the year. My little pocket calculator will not handle that equation. However, long hand still works. For those that like mind bogglers that will be: 5.886,938,432,000 miles a year, five trillion, eight hundred and eighty six billion, nine hundred and thirty eight million, four hundred and thirty two thousand miles. "A journey of a thousand miles, begins with a single step." -- Confusian Proverb-- Category:TreknicalCategory:Epiphany Trek